I'm very happy that you've asked these questions! I'll do my best to answer them:

1) "Listen, what horizon speaks". It's the personification of the horizon. And so it's just the horizon "who" is speaking

2) "Listen, only these simple moments" Yes, it's my mistake!!! Much better is your translation: "Listen to these simple moments only"
"Listen, also the heart has a voice" Again the personification, I've done literal translation and I think that it's well so, otherwise the meaning of this line would change too much.
3) "Elamise laul" is "song of living" (Or maybe it's better "song of the living"? I often have doubts about use of "the") "Elamise" is genitive case of the noun "elamine" and it means "living". I'm not able to explain it better...
If you have some other questions or you have discovered some mistakes in my translation, let me know!:)